In clinical trials and longitudinal studies, the outcome measures can often consist of: (1) the number of events and the multiple responses of the severity of these events: or (2) the time occurrences of events and the multiple responses of the severity corresponding to the events. In this proposal. this type of data is termed as randomly repeated outcome measures. The broad, long term objectives of this proposal are to develop statistical methods for analyzing data with randomly repeated outcome measures. For example, in the National Heart, Lung and Blood Institute TYPE II clinical trial, the outcome measures are obtained from patient's angiograms performed at the fifth year follow-up for patients with coronary artery disease. These measures are the numbers of vascular lesions (number of events) and the percentage of blockage of each lesion (severity of an event). The time occurrences of the lesions were unknown. In a longitudinal study conducted by the Centers for Disease Control and Prevention, the outcome measures are hospital admissions (time occurrences of events) and lengths of hospital stays (severity of these events) for perinatally infected children with human immunodeficiency virus (HIV). These two examples represent the data with randomly repeated outcome measures in cases (1) and (2), respectively. A change in disease status is often reflected by simultaneous changes in the number of the events and the multiple severity responses of these events (case (1)), or by simultaneous changes in the time occurrences of the events and the multiple severity responses of these events (case (2)). It is important to meaningfully model both of the outcome responses in this type of data in order to perform adequate comparisons of various treatments and effective evaluations of risk factors. However, very limited research has been done in this area. The methods proposed in this grant include likelihood-based models., marginal or random effects model, graphical diagnostics and goodness-of-fit tests for model fitting. Five different data sets in medical studies will be analyzed to demonstrate the usefulness of the proposed methods. The results from this research will provide medical researchers the much needed new statistical methods to analyze data with randomly repeated measures.